Proof: Angle Angle Side Triangle 2

Let's prove the following theorem:

if m∠ABC = m∠XYZ and m∠CAB = m∠ZXY and distance AC = distance XZ, then △BAC ≅ △YXZ

A C B X Z Y

Proof:

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Given
1 m∠ABC = m∠XYZ
2 m∠CAB = m∠ZXY
3 distance AC = distance XZ
Proof Table
# Claim Reason
1 m∠CBA = m∠ZYX if m∠ABC = m∠XYZ, then m∠CBA = m∠ZYX
2 m∠BAC = m∠YXZ if m∠CAB = m∠ZXY, then m∠BAC = m∠YXZ
3 △BAC ≅ △YXZ if m∠CBA = m∠ZYX and m∠BAC = m∠YXZ and distance AC = distance XZ, then △BAC ≅ △YXZ

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